If a and b are odd integers such that a-b > 7, what is the least possible positive difference between a and an even number less than b ?


I think that the question is mistakenly written. Shouldn't it read a - b > 8. This mistake threw my timing off.

Hey Goldie,

The question is properly written. This is how to solve it:

The difference between odd integers is always even. If a – b > 7, then the least possible positive difference between a and b is 8. Since b is odd, the largest even number less than b must be b – 1. So the least possible positive difference between a and b – 1 is 8 + 1, or 9.

The correct answer is D. An alternate strategy is to pick numbers: Let’s pick some numbers for a and b, minimizing the difference between them.

Suppose a = 11 and b = 3. Since 2 is the even number 1 less than 3, we are looking for the difference between 11 and 2, which is 9. Again, the correct answer is D.

Take care,
Steve

Thanks Steve !

I think I was just not thinking. It makes sense now.

You have not consider the -ve numbers, can you tell me why?

We've considered all numbers in the solution: positive, negative and 0, because we did not assume a sign of the numbers anywhere along the way.

In other words, the reasoning was done for ALL integers, including the negative ones.